Question: $\int (\sqrt[3]{x})^4\,dx=$ $+C$
Answer: At first it might seem as if we can't apply any rule we've learned to find the indefinite integral of a radical function. However, remember that any radical can be rewritten as a rational power. $\int (\sqrt[3]{x})^4\,dx=\int x^{^{\frac{4}{3}}}\,dx$ Now we can integrate using the reverse power rule: $\int x^n\,dx=\dfrac{x^{n+1}}{n+1}+C$ $\begin{aligned} \int (\sqrt[3]{x})^4\,dx&=\int x^{^{\frac{4}{3}}}\,dx \\\\ &=\dfrac{x^{^{\frac{4}{3}+1}}}{\dfrac{4}{3}+1}+C \\\\ &=\dfrac{3}{7} x^{^{\frac{7}{3}}}+C \end{aligned}$ In conclusion, $\int (\sqrt[3]{x})^4\,dx=\dfrac{3}{7} x^{^{\frac{7}{3}}}+C$